MATH 4753 Project 2

Abstract

This project is all about applications of SLR to real data using R

Tiffany Nguyen

1 My Video

2 Introduction

Here you should introduce the data and the problem you wish to solve. Use your own subheadings. Fill with informative sentences and pictures and links. You may inclucde sub-sub headings. You can cite from your bibliography Crawley (2012)

The data was collected here:

2.1 What are the variables?

data(mtcars)

library(DT)
datatable(
  mtcars,filter = 'top', options = list(
  pageLength = 5, autoWidth = TRUE, editable = TRUE, dom = 'Bfrtip',
    buttons = c('copy', 'csv', 'excel', 'pdf', 'print')),
caption = htmltools::tags$caption(
    style = 'caption-side: bottom; text-align: center;',
    'Table 2: ', htmltools::em('This is a simple caption for the table.')
  )
) %>%
  formatStyle('mpg',  color = 'red', backgroundColor = 'orange', fontWeight = 'bold')

library(crosstalk)
library(leaflet)
library(DT)

# Wrap data frame in SharedData
sd <- SharedData$new(quakes[sample(nrow(quakes), 100),])

# Create a filter input
filter_slider("mag", "Magnitude", sd, column=~mag, step=0.1, width=250)

Magnitude

# Use SharedData like a dataframe with Crosstalk-enabled widgets
bscols(
  leaflet(sd) %>% addTiles() %>% addMarkers(),
  datatable(sd, extensions="Scroller", style="bootstrap", class="compact", width="100%",
    options=list(deferRender=TRUE, scrollY=300, scroller=TRUE))
)

## Assuming "long" and "lat" are longitude and latitude, respectively

#devtools::install_github("jcheng5/d3scatter")

library(d3scatter)

shared_mtcars <- SharedData$new(mtcars)
bscols(widths = c(3,NA,NA),
  list(
    filter_checkbox("cyl", "Cylinders", shared_mtcars, ~cyl, inline = TRUE),
    filter_slider("hp", "Horsepower", shared_mtcars, ~hp, width = "100%"),
    filter_select("auto", "Automatic", shared_mtcars, ~ifelse(am == 0, "Yes", "No"))
  ),
  d3scatter(shared_mtcars, ~wt, ~mpg, ~factor(cyl), width="100%", height=250),
  d3scatter(shared_mtcars, ~hp, ~qsec, ~factor(cyl), width="100%", height=250)
)

Cylinders

4 6 8

Horsepower

Automatic

2.1.1 Sub sub headings can be useful

2.1.2 Plot data

library(ggplot2)
g = ggplot(mtcars, aes(x = disp, y = mpg, color = cyl)) + geom_point()
g = g + geom_smooth(method = "loess")
g

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation:
## colour.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Graph of data with loess smoother

2.2 How were the data collected?

2.3 What is the story behind the data?

2.4 Why was it gathered?

2.5 What is your interest in the data?

2.5.1 Include pictures ![](jpeg)

2.6 What problem do you wish to solve?

3 Theory needed to carry out SLR

3.1 Main result 1

3.2 Main result 2

3.3 Main result 3 etc

4 Validity with mathematical expressions

The following function was taken from https://rpubs.com/therimalaya/43190

4.1 Checks on validity

4.1.1 Straight trend line

4.1.1.1 Use trendscatter

4.1.2 Errors distributed Normally

\[\epsilon_i \sim N(0,\sigma^2)\]

4.1.2.1 Shapiro-wilk

4.1.3 Constant variance

4.1.3.1 Residual vs fitted values

4.1.3.2 trendscatter on Residual Vs Fitted

4.1.4 Zero mean value of \(\epsilon\)

4.1.5 Independence of data

5 Model selection if you compared models

5.1 Use adjusted \(R^2\)

\[R_{adj}^2 =\]

6 Analysis of the data

6.1 Make sure you include many great plots

6.2 Add the trend to the data

6.3 Summary lm object

6.3.1 Interpretation of all tests

6.3.2 Interpretation of multiple R squared

6.3.3 Interpretation of all point estimates

6.4 Calculate cis for \(\beta\) parameter estimates

6.4.1 Use of predict()

6.4.2 Use of ciReg()

6.4.3 Check on outliers using cooks plots

Remember to interpret this plot and all other plots

7 Conclusion

7.1 Answer your research question

7.2 Suggest ways to improve model or experiment

References

Crawley, Michael J. 2012. “Regression.” In The r Book, 449–97. Chichester, UK: John Wiley & Sons, Ltd.

Millar, Russell B. 2011. “Latent Variable Models.” In Statistics in Practice, 202–32. Chichester, UK: John Wiley & Sons, Ltd.